A Hitchhiker's Guide to the FFT

Introduction

There have been two main reasons to write this tutorial: a will to improve my webdesign skills and a feeling (after reading numerous forums) that there is a lot of misunderstanding around the fft.
It is also a way to develop a different, maybe more interactive, way of teaching. Finally, I want to mention that when writing this tutorial, I have been inspired by the excellent blog of Steve Eddins on the subject. I hope you will enjoy this tutorial.

In this case, \(F_c\) can be found analytically and is given by
$$\begin{aligned}
F_c (\Omega) & = \text{sinc}^2 (\Omega)\\
& = \left( \frac{\sin \left( \frac{\Omega}{2 \pi}
\right)}{\frac{\Omega}{2 \pi}} \right)^2
\end{aligned}$$
and can be plotted as follows: